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  1. M

    B Interference pattern, one particle at a time

    Well, OK, but the interaction has definite location, which means when the photon hit, it had definite location.
  2. M

    B Interference pattern, one particle at a time

    Anyway, I'm just trying to understand Nugatory's meaning when he says the photon has no position. Clearly, it has position when it interacts with the grain of light-sensitive material at a particular location on the screen. I do not mean to say that it has a definite position before then. It is...
  3. M

    B Interference pattern, one particle at a time

    <Sigh> Are you saying that the results of experiments involving photons never appear as one would expect were photons particles (like, say, dots on a screen) and never appear as one would expect were photons waves (like, say, diffraction patterns)? By "wave/particle duality," I do not have in...
  4. M

    B Interference pattern, one particle at a time

    Of course "sometimes." You run one kind of experiment, you get results that look like the results you'd expect were photons particles. You run another kind of experiment, you get results that look like the results you'd expect were photons waves. That's where the particle-wave duality originates.
  5. M

    B Interference pattern, one particle at a time

    As to a photon's "having no position" (I'll get to the rest after this is cleared up).... It is unclear to me what you mean. Here's my guess as to what you mean: the photon is a *something*--wavicle, vibrating string, something not well described as a particle but which, when observed, sometimes...
  6. M

    B Interference pattern, one particle at a time

    OK, here's my question. I frequently hear or read physicists say that the individual photons in the double-slit experiment interfere with themselves. But the individual photons strike the screen as individual dots, not as tiny interference patterns, don't they? And that means that what we see is...
  7. M

    B Interference pattern, one particle at a time

    [Mentor's note: Split off from another thread because it's a different question] I have a question about the single-photon double-slit experiment's results that isn't about the role of consciousness. Should I go ahead and ask it here or ask it elsewhere? (Briefly: If the results are lots of...
  8. M

    I Is quantum weirdness really weird?

    At least some (but possibly not all) of what seems weird in QM is the tendency to think of fundamental particles as though they were tiny billiard balls instead of something very different--as though they were property-carrying objects. Perhaps another way of viewing them would permit quantum...
  9. M

    Evolution did not start life

    I understand why someone might see a connection between Pasteur's experiment and a disproof of abiogenesis, but this misconception arises from a failure to understand what it was that Pasteur's experiment was designed to attempt to disprove and what it was not designed to attempt to disprove...
  10. M

    Consciousness and the Attention Schema Theory - Meaningful?

    One may imagine a computer's being fitted with optical sensing equipment, and one may imagine the computer's "attention" 's being focused on the optical information it is processing--and in one sense it would make sense to say that the computer need not be conscious, while in a second sense it...
  11. M

    Second postulate of SR quiz question

    Perhaps you could clarify what is meant by a two-way speed of light? If a beam of light strikes a mirror and gets bounced back, it travels at c (in vacuo) in each direction. I do not see why we must choose between thinking of c as the speed of light in vacuo, on one hand, and thinking of c as a...
  12. M

    Inequality with Logarithms

    In your attempt at a solution, you get ln (x + 1) >= ln (x - 1). From here you need to think about two things: (1) When is the ln function defined? (2) When is ln (a bigger number) >= ln (a smaller number)? Thinking about these should get you the solution.
  13. M

    Integral Evaluation with Partial Fractions

    Don't forget to treat the special case of alpha=1.
  14. M

    Isothermal vs Adiabatic expansion

    P1V1=P2V2 --> P1/P2 = V2/V1 P1V1^c = P2V2^c --> P1/P2 = V2^c/V1^c = (V2/V1)^c Holding P1 and V1 constant and taking c > 1, (V2/V1)^c gets big faster than does (V2/V1), so P2 gets small faster in the second equation than in the first.
  15. M

    Propositional logic help please

    No, no, no. The way the proof works is this: First, assume that a > 0. Demonstrate that under that assumption, one can derive a contradiction (the contradiction, in this case, being that for any epsilon > 0, a < epsilon, but that there exists an epsilon [namely, a/2] such that a > epsilon...
  16. M

    Propositional logic help please

    I don't see the previous post as helpful, since the problem statement is in the real numbers, not the natural numbers, so that the successorship relation doesn't seem to be pertinent. But you have that a < epsilon for any epsilon in R+. Suppose a does not equal 0. Then, since a is positive...
  17. M

    Propositional logic help please

    Yes, you can use a proof by contradiction. Suppose that a > 0 and then consider what happens if epsilon = a/2.
  18. M

    Polynomial division in Z5[x]

    > I found the remainder to be 4. If anyone has time, I believe I made a mistake somewhere and would like someone to attempt this division so I can check my work. If you have time please check it because I am not confident in dividing polynomials of different rings. Since (x+3)(x^3 + 2x^2 +...